Is it possible to recover deleted files in the file browser?
No.
Sorry :/
Blender only really has mechanisms for recovering blendfiles.
But wait..
Deleting files is likely fast because usually files are deleted by flipping a single bit which indicates to the operating system that this space is now available for use. The data is still there, but the longer you use the system the more likely it is some other program will overwrite it.
If you can, unmount/eject the drive until you can mount it read-only. If the disk in question is the one the OS is on, shut down the system and use a livecd (or an OS on another disk) to mount it (read-only, of course).
It's probable that can you can at least recover some of the files (possibly all) using conventional undelete methods such as photorec. How exactly to do this will depend on the format of filesystem your drive has, among other things. I recommend searching around for instructions for your specific operating system/filesystem.
Good luck!